分数次积分交换子在非齐Morrey空间上的紧性

本文主要建立由分数次积分$I_{\gamma}$与函数$b\in\mathrm{Lip}_{\beta}(\mu)$生成的交换子$[b, I_{\gamma}]$在以满足几何双倍与上部双倍条件的非齐度量测度空间为底空间的Morrey空间上紧性的充要条件.在假设控制函数$\lambda$满足逆双倍条件下,证明了交换子$[b,I_{\gamma}]$为从Morrey空间$M^{p}_{q}(\mu)$到$M^{s}_{t}(\mu)$紧性当且仅当$b\in\mathrm{Lip}_{\beta}(\mu)$.     

多线性分数次积分算子一般框架下的交换子的有界性——献给陆善镇教授75华诞

对任意给定的正整数m,Z^＋×{1,...,m}的任意一个有限子集S,定义一般化的多线性分数次积分算子的交换子Iα,→b,S（f）（x）=∫（Rn）^m ∏（i,j）∈S（bi（x）-bi（yj））/（｜x-y1｜＋…＋｜x-ym｜）^mn-α∏（j=1→m）fj（yj）d→y,其中d→y=dy1…dym.此框架下的交换子包含了以往研究的各类分数次积分算子的交换子,并蕴含了多线性背景下新的交换子形式.在上述非常一般框架下,本文给出带多重A→p,q权的多线性分数次积分算子的交换子Iα,→b,S（→f）的加权强型（L^p1（ω1）×···×L^pm（ωm）,L^q（ν→ωq））估计和加权弱型端点估计.本文还得到更一般核条件下的上述结果.     

粗糙核分数次积分算子的多线性算子在Hardy空间上的有界性

该文证明带有粗糙核的分数次积分算子的多线性算子\[T_{\Omega,\alpha}^{A}(f)(x)={\rm {\rm p.v.}}\int_{R^{n}}P_{m}(A;x,y)\frac{\Omega(x-y)}{|x-y|^{n-\alpha+m-1}}f(y){\rm d}y\]的$(H^{1}(\rr^{n}),L^{\frac{n}{n-\alpha},\infty}(\rr^{n}))$有界性.     

关于算子的Orlicz-Hardy空间

设$L$为$L^2({{\mathbb R}^n})$上的线性算子且$L$生成的解析半群 $\{e^{-tL}\}_{t\ge 0}$的核满足Poisson型上界估计, 其衰减性由$\theta(L)\in(0,\infty)$刻画. 又设$\omega$为定义在$(0,\infty)$上的$1$-\!上型及临界 $\widetilde p_0(\omega)$-\!下型函数, 其中 $\widetilde p_0(\omega)\in (n/(n+\theta(L)), 1]$. 并记 $\rho(t)={t^{-1}}/\omega^{-1}(t^{-1})$, 其中$t\in (0,\infty).$ 本文引入了一类 Orlicz-Hardy空间 $H_{\omega,\,L}({\mathbb R}^n)$及 $\mathrm{BMO}$-\!型空间${\mathrm{BMO}_{\rho,\,L} ({\mathbb R}^n)}$, 并建立了关于${\mathrm{BMO}_{\rho,\,L}({\mathbb R}^n)}$函数的John-Nirenberg不等式及 $H_{\omega,\,L}({\mathbb R}^n)$与 $\mathrm{BMO}_{\rho,\,L^\ast}({\mathbb R}^n)$的对偶关系, 其中 $L^\ast$为$L$在$L^2({\mathbb R}^n)$中的共轭算子. 利用该对偶关系, 本文进一步获得了$\mathrm{BMO}_{\rho,\,L^\ast}(\rn)$的$\ro$-\!Carleson 测度特征及 $H_{\omega,\,L}({\mathbb R}^n)$的分子特征, 并通过后者建立了广义分数次积分算子 $L^{-\gamma}_\rho$从$H_{\omega,\,L}({\mathbb R}^n)$到 $H_L^1({\mathbb R}^n)$或$L^q({\mathbb R}^n)$的有界性, 其中$q>1$, $H_L^1({\mathbb R}^n)$为Auscher, Duong 和 McIntosh引入的Hardy空间. 如取$\omega(t)=t^p$,其中$t\in(0,\infty)$及$p\in(n/(n+\theta(L)), 1]$, 则所得结果推广了已有的结果.     

分数次积分算子的交换子在齐型空间上的弱型估计

本文研究分数次积分交换子,其中Kα(x,y)=d(x,y)α-1,m∈N且b(x)∈BMO(X,μ),证明了Iα,bm是从Orlicz空间L(log L)m(X)到弱Lq(X)空间的映照．同时还证明了分数次极大算子交换子Mα,bm也有类似性质．     

变指标Lebesgue空间上的Marcinkiewicz积分高阶交换子

证明了一类Marcinkiewicz积分高阶交换子在变指标Lebesgue空间上的BMO和Lipschitz估计,对于分数次积分交换子也得到了类似的结果.     

混合径角$\lambda$中心有界平均振荡空间的一个特征

在这篇文章中,我们通过Hardy算子交换子$\mathrm{H}_b$与它的对偶算子交换子$\mathrm{H}^*_b$, 其中$b\in {\mathrm{CMOL}^{p_2, \lambda}_{\rm rad}L^{p_1}_{\rm ang}(\mathbb R^n)}$,建立了混合径角$\lambda$中心有界平均振荡空间的一个特征.     

分数次积分交换子的加权不等式

对分数次积分算子和BMO函数构成的高阶交换子, 该文给出了强型和弱型的加权不等式.     

Herz型空间上的分数次Hardy算子的交换子(英文)

本文主要对分数次Hardy算子和Lipschitz函数产生的交换子进行研究,得到了它在一类Herz型和Morrey-Herz型空间上的有界性.进一步还讨论了高阶交换子在这类空间上的有界性.     

高阶交换子在Hardy空间上的连续性

本文研究了由齐性分数次积分和BMO函数生成的高阶交换子在某些Hardy空间、弱Hardy空间和Herz型Hardy空间上的连续性.     

Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting

On the real line, the Dunkl operators$$D_{\nu}(f)(x):=\frac{d f(x)}{dx} + (2\nu+1) \frac{f(x) - f(-x)}{2x}, ~~ \quad\forall \, x \in \mathbb{R}, ~ \forall \, \nu \ge -\tfrac{1}{2}$$are differential-difference operators associated with the reflection group $\mathbb{Z}_2$ on $\mathbb{R}$, and on the $\mathbb{R}^d$ the Dunkl operators $\big\{D_{k,j}\big\}_{j=1}^{d}$ are the differential-difference operators associated with the reflection group $\mathbb{Z}_2^d$ on $\mathbb{R}^{d}$.In this paper, in the setting $\mathbb{R}$ we show that $b \in BMO(\mathbb{R},dm_{\nu})$ if and only if the maximal commutator $M_{b,\nu}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R},dm_{\nu})$. Also in the setting $\mathbb{R}^{d}$ we show that $b \in BMO(\mathbb{R}^{d},h_{k}^{2}(x) dx)$ if and only if the maximal commutator $M_{b,k}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R}^{d},h_{k}^{2}(x) dx)$.     

Lipschitz Estimates for Commutators of $N$-Dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator$\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0<α<1,1相似文献   

双线性分数次积分算子交换子在Morrey空间上有界的充分必要条件

In this paper,we obtain that b∈ BMO(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ.     

齐型空间上的Toeplitz型算子

设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性.     

一类分数阶微分方程多点边值问题解的存在性

本文讨论下面一类分数阶微分方程多点边值问题 $$\align &D^{\alpha}_{0+}u(t) = f(t, u(t),~D^{\alpha-1}_{0+}u(t), D^{\alpha-2}_{0+}u(t), D^{\alpha-3}_{0+}u(t)),~~t\in(0,1), \\&I^{4-\alpha}_{0+}u(0) = 0, ~D^{\alpha-1}_{0+}u(0)=\displaystyle{\sum_{i=1}^{m}}\alpha_{i}D^{\alpha-1}_{0+}u(\xi_{i}),\\&D^{\alpha-2}_{0+}u(1)=\sum\limits_ {j=1}^{n}\beta_{j} D^{\alpha-2}_{0+}u(\eta_{j}),~D^{\alpha-3}_{0+}u(1)-D^{\alpha-3}_{0+}u(0)=D^{\alpha-2}_{0+}u(\frac{1}{2}),\endalign$$其中$3<\alpha \leq 4$是一个实数.通过应用Mawhin重合度理论和构建适当的算子,得到了该边值问题解的存在性结果.     

分数次积分交换子在非齐Morrey空间上的紧性

The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_γ]which is generated by fractional integral I_γand function b∈Lip_β(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_γ]is compact from Morrey space M_q^p(μ)into Morrey space M_t^s(μ)if and only if b∈Lip_β(μ).     

Banach空间中有限个极大单调算子公共零点的迭代格式

令E为实光滑、一致凸Banach空间,E~*为其对偶空间．令A_i,B_i (?) E×E~*,i= 1,2,…,m,为极大单调算子且(?)(A_i~(-1)0∩B_i~(-1)0)≠φ．引入新的迭代算法,并利用Lyapunov泛函,Q_r算子与广义投影算子等技巧,证明迭代序列弱收敛于极大单调算子A_i,B_i,i= 1,2,…,m的公共零点的结论．     

Hardy Spaces and bmo on Manifolds with Bounded Geometry

We develop the theory of the “local” Hardy space and John-Nirenberg space when M is a Riemannian manifold with bounded geometry, building on the classic work of Fefferman-Stein and subsequent material, particularly of Goldberg and Ionescu. Results include – duality, L ^p estimates on an appropriate variant of the sharp maximal function, and bmo-Sobolev spaces, and action of a natural class of pseudodifferential operators, including a natural class of functions of the Laplace operator, in a setting that unifies these results with results on L ^p -Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive estimates for wave equations.      

Sharp Weighted Estimates for a Class of $n$-Dimensional Hardy-Steklov Operators

In this paper, we study one class of $n$-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding operator norms on both $L^p (\boldsymbol{R}^n)$ and BMO($\boldsymbol{R}^n$).     

Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$

In this paper we consider the Heckman-Opdam-Jacobi operator $∆_{HJ}$ on $\mathbb{R}^{d+1}.$ We define the Heckman-Opdam-Jacobi intertwining operator $V_{HJ},$ which turns out to be the transmutation operator between $∆_{HJ}$ and the Laplacian $∆_{d+1}.$ Next we construct $^tV_{HJ}$ the dual of this intertwining operator. We exploit these operators to develop a new harmonic analysis corresponding to $∆_{HJ}.$